A microwave amplifier has a noise figure (NF) of 3,text dB and gain of 20,text dB . A second stage has NF = 6,text dB . The cascaded noise figure by Friis formula is approximately:

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Electronics Engineering QUESTION #11711

Question 1

A microwave amplifier has a noise figure (NF) of $3\,\text{dB}$ and gain of $20\,\text{dB}$. A second stage has NF $= 6\,\text{dB}$. The cascaded noise figure by Friis formula is approximately:

$9\,\text{dB}$
$3.02\,\text{dB}$✔️
$4.5\,\text{dB}$
$6\,\text{dB}$

Correct Answer Explanation

Friis formula: $F_{total} = F_1 + \dfrac{F_2 - 1}{G_1}$. In linear: $F_1 = 10^{3/10} = 2$, $G_1 = 10^{20/10} = 100$, $F_2 = 10^{6/10} \approx 4$. $F_{total} = 2 + \dfrac{4-1}{100} = 2 + 0.03 = 2.03$. $\text{NF}_{total} = 10\log(2.03) \approx \mathbf{3.08\,\text{dB}}$. The first-stage NF dominates; high first-stage gain minimises the contribution of subsequent stages.

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